Converting the Sponza Palace ceiling into square-like faces
I would just go edit mode and do some manual cuts... it is enough to fix just a quarter of the mesh, then use a mirror modifier with X and Y axis enabled to recreate the ceiling.  

You have a couple of options to do the cuts:
1. K key is the knife tool, it got some useful extra keys, E to make multiple cuts, C to constraint, Ctrl to snap to to midpoint, SpaceBar to apply... do it from top view
2. J key is vertex connect path, just select endpoints of the arc and press J  

first option will result in more perfect squares and second one in a more organic distribution
for the tris I suggest to rotate the edges (Ctrl E > Rotate CW) and repeat with Shift R but you could just use Dissolve Edges

here's a blend with both of this techniques: https://www.dropbox.com/s/v7t730b506t8y30/ceiling.blend?dl=1